Explicitly correlated SCF study of small hydrides

Abstract

The "soft Coulomb hole" method of Chakravorty and Clementi has been implemented in a Gaussian lobe-orbital (GLO) program to include explicit electron-electron correlation in molecules according to a modified form of Coulomb's law in a program for workstations and personal computers (PCLOBE):Twice as many two-electron integrals must be calculated compared to the usual Hartree-Fock-Roothaan algorithm, but this "correlated self-consistent field (SCF)" method may be embedded within well-known SCF computer codes and yields more than 90% of the correlation energy in run times less than twice that of the restricted Hartree-Fock (RHF) method. A two-parameter model of correlation is calibrated on HF and LiH using the 6-311G * * basis as Gaussian lobe orbitals. The quantum Monte Carlo energies of LiH and HF were fitted to within 150 cal/mol, but the scaling model for first-row atoms is less good for H 2 . This work shows promise as a fast way to modify the Hartree-Fock-Roothaan method for accuracy approaching quantum Monte Carlo methods. This proof-of-concept work offers extension to modeling solvation properties of water solutions in high-pressure liquid chromatography (HPLC).

Explicitly correlated SCF study of anharmonic vibrations in (H2O)2

“…In both the GLO treatment by Otto et al and the previous Slater basis treatment of atoms by Chakravorty and Clementi [12], the w exponent was based on a formula in terms of orbital angular momentum with up to 12 parameters and this is a limitation for low-symmetry molecules. The CSCF method solves this problem by relating the w parameter to orbital scaling [9] with only two parameters. In the previous work [9], a lobe-equivalent basis set (6-311GL**) was developed to mimic the 6-311G** basis set previously optimized for correlation using Moller-Plesset fourth-order perturbation (MP4) [13].…”

“…The CSCF method solves this problem by relating the w parameter to orbital scaling [9] with only two parameters. In the previous work [9], a lobe-equivalent basis set (6-311GL**) was developed to mimic the 6-311G** basis set previously optimized for correlation using Moller-Plesset fourth-order perturbation (MP4) [13]. However, the lack of an energy derivative expression for the GLO basis requires use of finite difference techniques to obtain vibrational frequencies directly.…”

“…The CSCF method [9] depends on the two-electron integral derived by Otto et al [10] and Hernandez-Laguna et al [11] for Gaussian lobe basis (GLO) sets. In both the GLO treatment by Otto et al and the previous Slater basis treatment of atoms by Chakravorty and Clementi [12], the w exponent was based on a formula in terms of orbital angular momentum with up to 12 parameters and this is a limitation for low-symmetry molecules.…”

“…The GAMESS [14] normal mode output of eight significant figures was rounded to six places for input to PCLOBE because the normal mode printout from Gaussian 98 gave only two significant figures (Table I). The sum of atomic energies is an attempt at estimating what the sum of energies would be assuming the 6-311GL** basis [9] is close to the 6-311G** basis. Because this is a perturbation method, there is no firm bound to the anharmonicity correction.…”

“…The correlated-SCF [9] method replaces the Coulomb operator by a screened repulsion term parametrically related to orbital scaling using Eq. (1).…”